Superconducting Gap Renormalization around two Magnetic Impurities: From Shiba to Andreev Bound States

TL;DR

This paper investigates how two magnetic impurities affect the superconducting gap in an s-wave superconductor, revealing a transition from Shiba to Andreev bound states depending on impurity strength and spin orientation.

Contribution

It provides analytical and numerical insights into the gap renormalization caused by magnetic impurities, including the transition from Shiba to Andreev states.

Findings

Weakly bound Shiba states influence local gap renormalization.

Strong exchange coupling leads to a sign change in the local gap.

Transition from Shiba to Andreev bound states observed.

Abstract

We study the renormalization of the gap of an s-wave superconductor in the presence of two magnetic impurities. For weakly bound Shiba states, we analytically calculate the part of the gap renormalization that is sensitive to the relative orientation of the two impurity spins. For impurities with a strong exchange coupling to the conduction electrons, we solve the gap equation self-consistently by numerics and find that the sub-gap Shiba state turns into a supra-gap Andreev state when the local gap parameter changes sign under the impurities.